A salon and a cafe, 500 m apart, are situated between Natalie's house and Esther's house. The cafe is halfway between the two houses and the salon is closer to Esther's house. Natalie and Esther left their homes at the same time and arrived at the salon at the same time. Natalie drove at a speed of 72 km/h while Esther drove at a speed 10 km/h slower than Natalie. Leaving your answer in kilometres,

1. how much farther did Natalie travel than Esther?
2. how far is Esther's house from the cafe?

(a)
Let the distance between Natalie's house and Esther's house be 1 d.
Esther travelled = ¹₂ d - 500 m
Natalie travelled = ¹₂ d + 500 m

Distance that Natalie travelled more than Esther
= ¹₂ d + 500 - (¹₂ d - 500)
= ¹₂ d + 500 - ¹₂ d + 500
= 1000 m
= 1 km

(b)
Time that Natalie took to travel to the salon
= 1 ÷ 10
= ¹₁₀ h

Distance that Natalie travelled
= ¹₁₀ x 72
= 7.2 km

1000 m = 1 km
500 m = 0.5 km

Distance between Esther's house and the cafe
= 7.2 - 0.5
= 6.7 km

Answer(s): (a) 1 km; (b) 6.7 km